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On Chebyshev–Markov–Krein inequalities

✍ Scribed by A. Pinkus; J.M. Quesada

Book ID
116613801
Publisher
Elsevier Science
Year
2012
Tongue
English
Weight
248 KB
Volume
164
Category
Article
ISSN
0021-9045

No coin nor oath required. For personal study only.

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Denote by \(\eta_{i}=\cos (i \pi / n), i=0, \ldots, n\) the extreme points of the Chebyshev polynomial \(T_{n}(x)=\cos (n \operatorname{arc} \cos x)\). Let \(\pi_{n}\) be the set of real algebraic polynomials of degree not exceeding \(n\), and let \(B_{n}\) be the unit ball in the space \(\pi_{n}\)

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We give improved versions of Chebyshev's inequality for star-shaped sequencesi Valid • also for convex sequences.